Related papers: Turing patterns from dynamics of early HIV infecti…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
Dynamic models have been successfully used in producing estimates of HIV epidemics at national level, due to their epidemiological nature and their ability to simultaneously estimate prevalence, incidence, and mortality rates. Recently, HIV…
We revisit the SICA (Susceptible-Infectious-Chronic-AIDS) mathematical model for transmission dynamics of the human immunodeficiency virus (HIV) with varying population size in a homogeneously mixing population. We consider SICA models…
We study extended infection fronts advancing over a spatially uniform susceptible population by solving numerically a diffusive Kermack McKendrick SIR model with a dichotomous spatially random transmission rate, in two dimensions. We find a…
One way in which the human immunodeficiency virus (HIV-1) replicates within a host is by infecting activated CD4+ T-cells, which then produce additional copies of the virus. Even with the introduction of antiretroviral drug therapy, which…
Turing (or double-diffusive) instabilities describe pattern formation in reaction-diffusion systems, and were proposed in 1952 as a potential mechanism behind pattern formation in nature, such as leopard spots and zebra stripes. Because the…
We study minimal mean-field models of viral drug resistance development in which the efficacy of a therapy is described by a one-dimensional stochastic resetting process with mixed reflecting-absorbing boundary conditions. We derive…
The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…
Increasingly, experimentalists and modellers alike have come to recognise the important role of spatial structure in infection dynamics. Almost invariably, spatial computational models of viral infections - as with in vitro experimental…
Motivated by analogies between the spreading of human-to-human infections and of chemical processes, we develop a comprehensive model that accounts both for infection and for transport. In this analogy, the three different populations of…
The role of direct cell-to-cell spread in viral infections - where virions spread between host and susceptible cells without needing to be secreted into the extracellular environment - has come to be understood as essential to the dynamics…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
In [Math. Comput. Sci. 12 (2018), no. 2, 111--127], a delayed model describing the dynamics of the Human Immunodeficiency Virus (HIV) with Cytotoxic T Lymphocytes (CTL) immune response is investigated by Allali, Harroudi and Torres. Here,…
Tuberculosis (TB) and human immunodeficiency virus (HIV) can be considered a deadly human syndemic. In this article, we formulate a model for TB and HIV transmission dynamics. The model considers both TB and acquired immune deficiency…
We consider a general mathematical model of a within-host viral infection with $n$ virus strains and explicit age-since-infection structure for infected cells. In the model, multiple virus strains compete for a population of target cells.…
Dynamic models have been successfully used in producing estimates of HIV epidemics at the national level due to their epidemiological nature and their ability to estimate prevalence, incidence, and mortality rates simultaneously. Recently,…
Infectious diseases outbreaks are often characterized by a spatial component induced by hosts' distribution, mobility, and interactions. Spatial models that incorporate hosts' movements are being used to describe these processes, to…
When modelling HIV epidemics, it is important to incorporate set-point viral load and its heritability. As set-point viral load distributions can differ significantly amongst epidemics, it is imperative to account for the observed local…
We consider a mathematical model comprising of four coupled ordinary differential equations (ODEs) for studying the hepatitis C (HCV) viral dynamics. The model embodies the efficacies of a combination therapy of interferon and ribavirin. A…